Elementary School Math Quiz: Multiply Fractions By Whole Numbers

20 questions · exam conditions

0:00

Multiply Fractions By Whole NumbersQuestion 1 of 20

A recipe calls for $\frac{2}{5}$ cup of flour. Jake wants to make 3 batches of the recipe, but he only has a $\frac{1}{5}$ cup measuring scoop. How many scoops of flour will Jake need?

5 scoops of flour total

6 scoops of flour total

8 scoops of flour total

10 scoops of flour total

← Back to quizzes

Elementary School Math Quiz

Elementary School Math Quiz: Multiply Fractions By Whole Numbers

Practice Multiply Fractions By Whole Numbers in Elementary School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Multiply Fractions By Whole Numbers, giving you a quick way to practice the rules, question types, and explanations that matter most for Elementary School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A recipe calls for $\frac{2}{5}$ cup of flour. Jake wants to make 3 batches of the recipe, but he only has a $\frac{1}{5}$ cup measuring scoop. How many scoops of flour will Jake need?

5 scoops of flour total
6 scoops of flour total (correct answer)
8 scoops of flour total
10 scoops of flour total

Explanation: Jake needs

3 \times \frac{2}{5} = \frac{6}{5}

cups total. Since each scoop is

\frac{1}{5}

cup, he needs

\frac{6}{5} \div \frac{1}{5} = 6

scoops. Choice A uses

\frac{2}{5} \times 5 = 2

batches plus 3 extra. Choice C incorrectly adds

3 + 2 + 3 = 8

. Choice D uses

2 \times 5 = 10

Question 2

What is $8 \times \frac{5}{12}$ ?

$13/12$
$5/96$
$40/12$ (correct answer)
$40/96$

Explanation: Multiplying a whole number by a fraction means multiplying the whole number by the numerator and keeping the denominator:

8 \times 5 = 40

, so the product is

40/12

. Choice A comes from adding 8 and 5 instead of multiplying them. Choice B mistakenly multiplies the denominators together instead of keeping the original denominator. Choice D multiplies both the numerator and denominator by 8, which changes the value unnecessarily. Choice C correctly applies the rule for multiplying a whole number by a fraction.

Question 3

Sofia pours $\frac{4}{7}$ liter of water into each bottle. She fills 3 bottles. What is $3 \times \left(\frac{4}{7}\right)$ ? Use $n \times \left(\frac{a}{b}\right) = \frac{n \times a}{b}$ .

$\frac{12}{21}$
$\frac{12}{7}$ (correct answer)
$\frac{4}{21}$
$\frac{7}{7}$

Explanation: The correct answer is 12/7, because 3 times 4/7 equals (3 times 4)/7, which is 12/7. Choice A, 12/21, mistakenly multiplies both the numerator and denominator by 3 instead of just the numerator. Choice C, 4/21, multiplies the denominator by 3 but leaves the numerator too small, losing track of all three bottles. Choice D, 7/7, comes from adding the numerator and denominator instead of multiplying by 3.

Question 4

What is $7 \times \frac{1}{4}$ ?

$7/4$ (correct answer)
$7/28$
$1/28$
$8/4$

Explanation: Multiplying a whole number by a fraction means multiplying the whole number by the numerator and keeping the denominator:

7 \times 1 = 7

, so the product is

7/4

. Choice B multiplies both the numerator and the denominator by 7, which changes the value unnecessarily. Choice C uses only the denominator multiplication without adjusting the numerator, giving a much smaller value. Choice D comes from adding 7 and 1 instead of multiplying them. Choice A correctly applies the rule for multiplying a whole number by a fraction.

Question 5

Multiply $7 \times \left(\frac{2}{9}\right)$ . Show you understand that $\frac{2}{9} = 2 \times \left(\frac{1}{9}\right)$ , so the total is $(7 \times 2)$ ninths.

$\frac{2}{63}$
$\frac{14}{63}$
$\frac{14}{9}$ (correct answer)
$\frac{9}{9}$

Explanation: Multiplying a whole number by a fraction means multiplying the whole number by the numerator:

7 \times 2 = 14

, keeping the denominator 9, giving

\frac{14}{9}

. Choice A comes from multiplying the denominators together instead of the numerator by the whole number. Choice B multiplies both the numerator and denominator by 7, which changes the value unnecessarily. Choice D comes from adding 7 and 2 to get 9 and mistakenly using that as both parts of the fraction. Choice C correctly applies the rule for multiplying a whole number by a fraction.

Question 6

Multiply $8 \times \left(\frac{1}{6}\right)$ . Think of this as 8 groups of the unit fraction $\frac{1}{6}$ .

$\frac{8}{6}$ (correct answer)
$\frac{1}{48}$
$\frac{9}{6}$
$\frac{8}{48}$

Explanation: This question tests 4th grade understanding of multiplying a fraction by a whole number using the principle that n × (a/b) = (n × a)/b, recognizing this as a multiple of the unit fraction 1/b (CCSS.4.NF.4.b). To multiply a whole number by a fraction, we multiply the whole number by the numerator and keep the denominator the same: n × (a/b) = (n × a)/b. This works because a/b is really a copies of the unit fraction 1/b, so n groups of (a copies of 1/b) equals (n × a) copies of 1/b, which equals (n × a)/b. For example, 8 × (1/6) means 8 groups of one-sixth, which equals 8 sixths total, or 8/6. To multiply 8 × (1/6), we multiply 8 × 1 = 8, and keep the denominator 6, giving 8/6. We can also see this as 8 groups of 1 unit fraction (1/6), which equals 8 unit fractions = 8 × (1/6) = 8/6. Choice A is correct because multiplying: 8 × 1 = 8, keeping denominator 6: 8/6; using unit fractions: 8 × (1 × (1/6)) = (8 × 1) × (1/6) = 8 × (1/6) = 8/6; repeated addition: 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 8/6. This demonstrates understanding that multiplying by whole number affects numerator only. Choice C represents multiplying both numerator and denominator by 8, giving 8/48, which happens when students incorrectly think both parts multiply by n. To help students: Use formula n × (a/b) = (n × a)/b—multiply the NUMERATOR by whole number, KEEP DENOMINATOR same. Show why: a/b is 'a copies of 1/b,' so n groups of that is (n × a) copies of 1/b = (n × a)/b. Use visuals: draw 8 groups of 1/6 (eight shaded sixths), count total sixths: 8 sixths = 8/6. Practice with unit fractions first: 8 × (1/6) = 8/6 (easier to see). Connect to repeated addition: 8 × (1/6) = 1/6 + 1/6 + ... (8 times) = 8/6. Convert improper fractions to mixed numbers for interpretation: 8/6 = 1 2/6 = 1 1/3. Watch for: multiplying denominator (wrong), adding instead of multiplying, arithmetic errors in numerator multiplication, and forgetting that denominator stays the same.

Question 7

What is $5 \times \left(\frac{3}{10}\right)$ written as a fraction?

$\frac{15}{50}$
$\frac{3}{50}$
$\frac{15}{10}$ (correct answer)
$\frac{8}{10}$

Explanation: Multiplying a whole number by a fraction scales the numerator: 5 x 3 = 15, so 5 x (3/10) = 15/10. Choice A multiplies both the numerator and denominator by 5 instead of only the numerator. Choice B multiplies the denominator instead of the numerator. Choice D reflects an addition-based error rather than multiplication.

Question 8

Multiply $2\times\left(\tfrac{7}{12}\right)$ using $n\times\left(\tfrac{a}{b}\right)=\tfrac{n\times a}{b}$ . Your answer may be an improper fraction.

$\tfrac{14}{24}$
$\tfrac{7}{24}$
$\tfrac{14}{12}$ (correct answer)
$\tfrac{9}{12}$

Explanation: Using n times a/b equals (n times a)/b, multiplying 2 by 7/12 gives 14/12, so Choice C is correct. Choice A, 14/24, comes from multiplying the denominator by 2 as well as the numerator, instead of keeping the denominator the same. Choice B, 7/24, comes from keeping the numerator the same and multiplying only the denominator by 2. Choice D, 9/12, comes from adding 2 to the numerator instead of multiplying it by 2. Multiplying only the numerator by the whole number, and keeping the denominator the same, gives the correct product.

Question 9

Sofia pours $3$ equal cups of juice. Each cup is $\tfrac{5}{6}$ of a liter. What is the total amount of juice?

$\tfrac{8}{6}$
$\tfrac{15}{18}$
$\tfrac{5}{18}$
$\tfrac{15}{6}$ (correct answer)

Explanation: Multiplying 3 cups by

\tfrac{5}{6}

liter per cup means multiplying 3 by the numerator, 5, to get 15, while keeping the denominator 6, giving

\tfrac{15}{6}

. Choice A comes from adding 3 and 5 instead of multiplying them. Choice B multiplies both the numerator and the denominator by 3, which changes the value unnecessarily. Choice C multiplies the denominators together instead of keeping the original denominator. Choice D correctly applies the rule for multiplying a whole number by a fraction.

Question 10

Keisha makes 4 batches of trail mix. Each batch uses $\frac{3}{8}$ cup of raisins. What is $4 \times \left(\frac{3}{8}\right)$ ? Use $n \times \left(\frac{a}{b}\right) = \frac{n \times a}{b}$ .

$\frac{7}{8}$
$\frac{12}{32}$
$\frac{12}{8}$ (correct answer)
$\frac{3}{32}$

Explanation: The correct answer is 12/8, because 4 times 3/8 equals (4 times 3)/8, which is 12/8. Choice A, 7/8, comes from adding 4 and 3 instead of multiplying them. Choice B, 12/32, mistakenly multiplies both the numerator and denominator by 4 instead of just the numerator. Choice D, 3/32, comes from multiplying the denominator by 4 while leaving the numerator unchanged, then losing track of the original numerator value.

Question 11

Which expression shows the same value as $5 \times \frac{4}{7}$ using unit fractions?

$5 + 4 \times \frac{1}{7}$
$5 \times \frac{1}{7}$
$20 \times \frac{1}{4}$
$5 \times 4 \times \frac{1}{7}$ (correct answer)

Explanation: The correct answer is D because

\frac{4}{7}

is 4 copies of the unit fraction

\frac{1}{7}

, so 5 groups of that is

5 \times 4 \times \frac{1}{7}

. Choice A adds the 5 instead of multiplying. Choice B leaves out the 4 copies of

\frac{1}{7}

. Choice C uses the wrong unit fraction,

\frac{1}{4}

instead of

\frac{1}{7}

Question 12

Study the equation: $4 \times \frac{a}{5} = \frac{12}{5}$ . What value of $a$ makes this equation true?

$a = 3$ (correct answer)
$a = 8$
$a = 12$
$a = 48$

Explanation:

a = 3

is correct because

4 \times \frac{3}{5} = \frac{12}{5}

a = 8

is incorrect because

4 \times \frac{8}{5}

does not equal

\frac{12}{5}

a = 12

is incorrect because it skips dividing by 4.

a = 48

is incorrect because it multiplies instead of dividing to isolate

a

Question 13

Carlos ran $\frac{5}{8}$ of a mile each day for 3 days. Maya ran $\frac{3}{8}$ of a mile each day for 5 days. Who ran farther?

Carlos ran farther
Maya ran farther
They ran the same distance (correct answer)
Not enough information

Explanation: They ran the same distance because Carlos ran

3 \times \frac{5}{8} = \frac{15}{8}

miles and Maya ran

5 \times \frac{3}{8} = \frac{15}{8}

miles. Carlos ran farther is incorrect because the two totals are equal. Maya ran farther is incorrect for the same reason. Not enough information is incorrect because both totals can be calculated from the given facts.

Question 14

Maria has $\frac{3}{8}$ of a pizza. She wants to make 4 lunch portions, each $\frac{3}{8}$ of a pizza. How much pizza will Maria need in total?

$\frac{7}{8}$ of a pizza
$\frac{12}{8}$ of a pizza (correct answer)
$\frac{4}{11}$ of a pizza
$\frac{12}{32}$ of a pizza

Explanation: Maria needs 12/8 of a pizza because 4 portions of 3/8 each means 4 times 3/8, which equals 12/8. Choice A adds 3/8 + 4/8 rather than multiplying. Choice C incorrectly multiplies the denominators together for a nonsensical result. Choice D multiplies both the numerator and denominator by 4, which doesn't represent repeated addition correctly.

Question 15

A whole shape is divided into sixths. If 7 of these one-sixth pieces are shaded across one or more wholes, what multiplication expression represents the total shaded amount?

$7 \times \frac{1}{6}$ (correct answer)
$6 \times \frac{1}{7}$
$8 \times \frac{1}{6}$
$6 \times \frac{1}{8}$

Explanation: 7 shaded one-sixth pieces means the total is 7 groups of 1/6, or 7 × 1/6. Choice B swaps the roles of the piece count and the piece size. Choice C uses 8 instead of the actual count of 7 shaded pieces. Choice D also swaps which number represents the pieces and which represents the size of each piece.

Question 16

What is $5 \times \tfrac{2}{3}$ ?

$10/3$ (correct answer)
$2/15$
$10/15$
$7/3$

Explanation: The correct answer is A, 10/3, because 5 times 2/3 equals 10/3. Choice B, 2/15, comes from multiplying the denominators together instead of multiplying the numerator by 5. Choice C, 10/15, comes from also multiplying the denominator by 5 instead of keeping it the same. Choice D, 7/3, comes from adding 5 and 2/3 instead of multiplying.

Question 17

Keisha makes 6 batches of trail mix. Each batch uses $3/10$ cup of raisins. What is $6 \times (3/10)$ cups in all? Use $6 \times (a/b) = (6 \times a)/b$ .

$18/10$ (correct answer)
$3/60$
$18/60$
$9/10$

Explanation: The correct answer is 18/10, because 6 times 3/10 equals (6 times 3)/10, which is 18/10. Choice B, 3/60, mistakenly multiplies the denominator by 6 instead of the numerator. Choice C, 18/60, multiplies both the numerator and denominator by 6 instead of just the numerator. Choice D, 9/10, comes from adding 6 and 3 instead of multiplying them.

Question 18

Carlos walks $9$ laps. Each lap is $\tfrac{2}{5}$ mile. What is the total distance Carlos walks?

$\tfrac{18}{5}$ (correct answer)
$\tfrac{2}{45}$
$\tfrac{11}{5}$
$\tfrac{18}{45}$

Explanation: The correct answer is A, 18/5 miles, because 9 times 2/5 equals 18/5. Choice B, 2/45, comes from multiplying the denominators together instead of multiplying the numerator by 9. Choice C, 11/5, comes from adding 9 and 2/5 instead of multiplying. Choice D, 18/45, comes from also multiplying the denominator by 9 instead of keeping it the same.

Question 19

Carlos pours 4 equal servings of juice. Each serving is 2/11 liter. What is 4 x (2/11) liters? Use 4 x (2/11) = (4 x 2)/11.

2/44
6/11
8/44
8/11 (correct answer)

Explanation: Multiplying 4 by 2/11 means multiplying the numerator by 4 while keeping the denominator the same: (4 x 2)/11 = 8/11. Choice A (2/44) comes from multiplying the denominator instead of the numerator. Choice C (8/44) multiplies both the numerator and denominator by 4. Choice B (6/11) doesn't match the multiplication shown in the problem.

Question 20

Keisha fills 5 small jars. Each jar holds $\tfrac{2}{7}$ cup of beads. What is the total amount of beads, in cups?

$\tfrac{7}{10}$
$\tfrac{10}{7}$ (correct answer)
$\tfrac{10}{35}$
$\tfrac{2}{35}$

Explanation: Five jars holding 2/7 cup each gives 5 x (2/7) = 10/7 cups total. Choice A swaps the numerator and denominator, giving an incorrect fraction. Choice C multiplies both the numerator and denominator by 5 instead of only the numerator, so it does not represent multiplication correctly. Choice D only multiplies the denominator, which shrinks the fraction instead of scaling it up.